LMFDB - Embedded newform 4334.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.32608 q^{3} +1.00000 q^{4} +3.07836 q^{5} +3.32608 q^{6} -4.99294 q^{7} -1.00000 q^{8} +8.06282 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.32608 q^{3} +1.00000 q^{4} +3.07836 q^{5} +3.32608 q^{6} -4.99294 q^{7} -1.00000 q^{8} +8.06282 q^{9} -3.07836 q^{10} +1.00000 q^{11} -3.32608 q^{12} +5.67732 q^{13} +4.99294 q^{14} -10.2389 q^{15} +1.00000 q^{16} +5.97827 q^{17} -8.06282 q^{18} +2.29990 q^{19} +3.07836 q^{20} +16.6069 q^{21} -1.00000 q^{22} +8.31678 q^{23} +3.32608 q^{24} +4.47627 q^{25} -5.67732 q^{26} -16.8393 q^{27} -4.99294 q^{28} +6.11844 q^{29} +10.2389 q^{30} +9.96380 q^{31} -1.00000 q^{32} -3.32608 q^{33} -5.97827 q^{34} -15.3701 q^{35} +8.06282 q^{36} -7.89255 q^{37} -2.29990 q^{38} -18.8832 q^{39} -3.07836 q^{40} -0.533742 q^{41} -16.6069 q^{42} -0.546558 q^{43} +1.00000 q^{44} +24.8202 q^{45} -8.31678 q^{46} +6.46522 q^{47} -3.32608 q^{48} +17.9295 q^{49} -4.47627 q^{50} -19.8842 q^{51} +5.67732 q^{52} +0.736628 q^{53} +16.8393 q^{54} +3.07836 q^{55} +4.99294 q^{56} -7.64966 q^{57} -6.11844 q^{58} +10.4071 q^{59} -10.2389 q^{60} -4.39424 q^{61} -9.96380 q^{62} -40.2572 q^{63} +1.00000 q^{64} +17.4768 q^{65} +3.32608 q^{66} +6.05610 q^{67} +5.97827 q^{68} -27.6623 q^{69} +15.3701 q^{70} +2.94367 q^{71} -8.06282 q^{72} -10.6891 q^{73} +7.89255 q^{74} -14.8884 q^{75} +2.29990 q^{76} -4.99294 q^{77} +18.8832 q^{78} -5.64779 q^{79} +3.07836 q^{80} +31.8206 q^{81} +0.533742 q^{82} +2.69238 q^{83} +16.6069 q^{84} +18.4032 q^{85} +0.546558 q^{86} -20.3504 q^{87} -1.00000 q^{88} +11.9330 q^{89} -24.8202 q^{90} -28.3465 q^{91} +8.31678 q^{92} -33.1404 q^{93} -6.46522 q^{94} +7.07992 q^{95} +3.32608 q^{96} -14.3699 q^{97} -17.9295 q^{98} +8.06282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.32608	−1.92031	−0.960157	−	0.279461i	$-0.909844\pi$
$3$	−3.32608	−1.92031	−0.960157	+	0.279461i	$0.909844\pi$
$4$	1.00000	0.500000
$5$	3.07836	1.37668	0.688341	−	0.725387i	$-0.258339\pi$
$5$	3.07836	1.37668	0.688341	+	0.725387i	$0.258339\pi$
$6$	3.32608	1.35787
$7$	−4.99294	−1.88716	−0.943578	−	0.331151i	$-0.892563\pi$
$7$	−4.99294	−1.88716	−0.943578	+	0.331151i	$0.892563\pi$
$8$	−1.00000	−0.353553
$9$	8.06282	2.68761
$10$	−3.07836	−0.973461
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.32608	−0.960157
$13$	5.67732	1.57460	0.787302	−	0.616567i	$-0.211477\pi$
$13$	5.67732	1.57460	0.787302	+	0.616567i	$0.211477\pi$
$14$	4.99294	1.33442
$15$	−10.2389	−2.64366
$16$	1.00000	0.250000
$17$	5.97827	1.44994	0.724971	−	0.688779i	$-0.241853\pi$
$17$	5.97827	1.44994	0.724971	+	0.688779i	$0.241853\pi$
$18$	−8.06282	−1.90042
$19$	2.29990	0.527634	0.263817	−	0.964573i	$-0.415019\pi$
$19$	2.29990	0.527634	0.263817	+	0.964573i	$0.415019\pi$
$20$	3.07836	0.688341
$21$	16.6069	3.62393
$22$	−1.00000	−0.213201
$23$	8.31678	1.73417	0.867084	−	0.498162i	$-0.165992\pi$
$23$	8.31678	1.73417	0.867084	+	0.498162i	$0.165992\pi$
$24$	3.32608	0.678934
$25$	4.47627	0.895255
$26$	−5.67732	−1.11341
$27$	−16.8393	−3.24073
$28$	−4.99294	−0.943578
$29$	6.11844	1.13617	0.568083	−	0.822971i	$-0.307685\pi$
$29$	6.11844	1.13617	0.568083	+	0.822971i	$0.307685\pi$
$30$	10.2389	1.86935
$31$	9.96380	1.78955	0.894776	−	0.446516i	$-0.147335\pi$
$31$	9.96380	1.78955	0.894776	+	0.446516i	$0.147335\pi$
$32$	−1.00000	−0.176777
$33$	−3.32608	−0.578996
$34$	−5.97827	−1.02526
$35$	−15.3701	−2.59801
$36$	8.06282	1.34380
$37$	−7.89255	−1.29753	−0.648764	−	0.760990i	$-0.724714\pi$
$37$	−7.89255	−1.29753	−0.648764	+	0.760990i	$0.724714\pi$
$38$	−2.29990	−0.373093
$39$	−18.8832	−3.02373
$40$	−3.07836	−0.486731
$41$	−0.533742	−0.0833564	−0.0416782	−	0.999131i	$-0.513270\pi$
$41$	−0.533742	−0.0833564	−0.0416782	+	0.999131i	$0.513270\pi$
$42$	−16.6069	−2.56251
$43$	−0.546558	−0.0833493	−0.0416746	−	0.999131i	$-0.513269\pi$
$43$	−0.546558	−0.0833493	−0.0416746	+	0.999131i	$0.513269\pi$
$44$	1.00000	0.150756
$45$	24.8202	3.69998
$46$	−8.31678	−1.22624
$47$	6.46522	0.943049	0.471525	−	0.881853i	$-0.343704\pi$
$47$	6.46522	0.943049	0.471525	+	0.881853i	$0.343704\pi$
$48$	−3.32608	−0.480078
$49$	17.9295	2.56136
$50$	−4.47627	−0.633041
$51$	−19.8842	−2.78435
$52$	5.67732	0.787302
$53$	0.736628	0.101184	0.0505918	−	0.998719i	$-0.483889\pi$
$53$	0.736628	0.101184	0.0505918	+	0.998719i	$0.483889\pi$
$54$	16.8393	2.29154
$55$	3.07836	0.415085
$56$	4.99294	0.667210
$57$	−7.64966	−1.01322
$58$	−6.11844	−0.803390
$59$	10.4071	1.35489	0.677443	−	0.735576i	$-0.263088\pi$
$59$	10.4071	1.35489	0.677443	+	0.735576i	$0.263088\pi$
$60$	−10.2389	−1.32183
$61$	−4.39424	−0.562625	−0.281312	−	0.959616i	$-0.590770\pi$
$61$	−4.39424	−0.562625	−0.281312	+	0.959616i	$0.590770\pi$
$62$	−9.96380	−1.26540
$63$	−40.2572	−5.07193
$64$	1.00000	0.125000
$65$	17.4768	2.16773
$66$	3.32608	0.409412
$67$	6.05610	0.739870	0.369935	−	0.929058i	$-0.379380\pi$
$67$	6.05610	0.739870	0.369935	+	0.929058i	$0.379380\pi$
$68$	5.97827	0.724971
$69$	−27.6623	−3.33015
$70$	15.3701	1.83707
$71$	2.94367	0.349350	0.174675	−	0.984626i	$-0.444113\pi$
$71$	2.94367	0.349350	0.174675	+	0.984626i	$0.444113\pi$
$72$	−8.06282	−0.950212
$73$	−10.6891	−1.25107	−0.625534	−	0.780197i	$-0.715119\pi$
$73$	−10.6891	−1.25107	−0.625534	+	0.780197i	$0.715119\pi$
$74$	7.89255	0.917491
$75$	−14.8884	−1.71917
$76$	2.29990	0.263817
$77$	−4.99294	−0.568999
$78$	18.8832	2.13810
$79$	−5.64779	−0.635426	−0.317713	−	0.948187i	$-0.602915\pi$
$79$	−5.64779	−0.635426	−0.317713	+	0.948187i	$0.602915\pi$
$80$	3.07836	0.344171
$81$	31.8206	3.53562
$82$	0.533742	0.0589419
$83$	2.69238	0.295527	0.147763	−	0.989023i	$-0.452793\pi$
$83$	2.69238	0.295527	0.147763	+	0.989023i	$0.452793\pi$
$84$	16.6069	1.81197
$85$	18.4032	1.99611
$86$	0.546558	0.0589369
$87$	−20.3504	−2.18179
$88$	−1.00000	−0.106600
$89$	11.9330	1.26490	0.632449	−	0.774602i	$-0.282050\pi$
$89$	11.9330	1.26490	0.632449	+	0.774602i	$0.282050\pi$
$90$	−24.8202	−2.61628
$91$	−28.3465	−2.97152
$92$	8.31678	0.867084
$93$	−33.1404	−3.43650
$94$	−6.46522	−0.666836
$95$	7.07992	0.726384
$96$	3.32608	0.339467
$97$	−14.3699	−1.45904	−0.729519	−	0.683960i	$-0.760256\pi$
$97$	−14.3699	−1.45904	−0.729519	+	0.683960i	$0.760256\pi$
$98$	−17.9295	−1.81115
$99$	8.06282	0.810344
$100$	4.47627	0.447627
$101$	−3.65568	−0.363754	−0.181877	−	0.983321i	$-0.558217\pi$
$101$	−3.65568	−0.363754	−0.181877	+	0.983321i	$0.558217\pi$
$102$	19.8842	1.96883
$103$	2.71822	0.267834	0.133917	−	0.990993i	$-0.457244\pi$
$103$	2.71822	0.267834	0.133917	+	0.990993i	$0.457244\pi$
$104$	−5.67732	−0.556707
$105$	51.1221	4.98900
$106$	−0.736628	−0.0715477
$107$	10.9451	1.05810	0.529052	−	0.848589i	$-0.322547\pi$
$107$	10.9451	1.05810	0.529052	+	0.848589i	$0.322547\pi$
$108$	−16.8393	−1.62037
$109$	−2.56588	−0.245766	−0.122883	−	0.992421i	$-0.539214\pi$
$109$	−2.56588	−0.245766	−0.122883	+	0.992421i	$0.539214\pi$
$110$	−3.07836	−0.293510
$111$	26.2513	2.49166
$112$	−4.99294	−0.471789
$113$	−6.00200	−0.564621	−0.282310	−	0.959323i	$-0.591101\pi$
$113$	−6.00200	−0.564621	−0.282310	+	0.959323i	$0.591101\pi$
$114$	7.64966	0.716456
$115$	25.6020	2.38740
$116$	6.11844	0.568083
$117$	45.7752	4.23192
$118$	−10.4071	−0.958048
$119$	−29.8492	−2.73627
$120$	10.2389	0.934676
$121$	1.00000	0.0909091
$122$	4.39424	0.397836
$123$	1.77527	0.160071
$124$	9.96380	0.894776
$125$	−1.61222	−0.144201
$126$	40.2572	3.58640
$127$	−5.12157	−0.454466	−0.227233	−	0.973840i	$-0.572968\pi$
$127$	−5.12157	−0.454466	−0.227233	+	0.973840i	$0.572968\pi$
$128$	−1.00000	−0.0883883
$129$	1.81790	0.160057
$130$	−17.4768	−1.53282
$131$	−16.7004	−1.45912	−0.729560	−	0.683917i	$-0.760275\pi$
$131$	−16.7004	−1.45912	−0.729560	+	0.683917i	$0.760275\pi$
$132$	−3.32608	−0.289498
$133$	−11.4833	−0.995727
$134$	−6.05610	−0.523167
$135$	−51.8375	−4.46146
$136$	−5.97827	−0.512632
$137$	0.0565638	0.00483257	0.00241629	−	0.999997i	$-0.499231\pi$
$137$	0.0565638	0.00483257	0.00241629	+	0.999997i	$0.499231\pi$
$138$	27.6623	2.35477
$139$	−12.9949	−1.10222	−0.551108	−	0.834434i	$-0.685795\pi$
$139$	−12.9949	−1.10222	−0.551108	+	0.834434i	$0.685795\pi$
$140$	−15.3701	−1.29901
$141$	−21.5038	−1.81095
$142$	−2.94367	−0.247028
$143$	5.67732	0.474761
$144$	8.06282	0.671901
$145$	18.8347	1.56414
$146$	10.6891	0.884639
$147$	−59.6350	−4.91861
$148$	−7.89255	−0.648764
$149$	14.2046	1.16368	0.581841	−	0.813302i	$-0.302333\pi$
$149$	14.2046	1.16368	0.581841	+	0.813302i	$0.302333\pi$
$150$	14.8884	1.21564
$151$	15.6989	1.27756	0.638780	−	0.769389i	$-0.279439\pi$
$151$	15.6989	1.27756	0.638780	+	0.769389i	$0.279439\pi$
$152$	−2.29990	−0.186547
$153$	48.2017	3.89687
$154$	4.99294	0.402343
$155$	30.6721	2.46364
$156$	−18.8832	−1.51187
$157$	−6.70996	−0.535513	−0.267757	−	0.963487i	$-0.586282\pi$
$157$	−6.70996	−0.535513	−0.267757	+	0.963487i	$0.586282\pi$
$158$	5.64779	0.449314
$159$	−2.45009	−0.194304
$160$	−3.07836	−0.243365
$161$	−41.5252	−3.27264
$162$	−31.8206	−2.50006
$163$	−1.54140	−0.120732	−0.0603658	−	0.998176i	$-0.519227\pi$
$163$	−1.54140	−0.120732	−0.0603658	+	0.998176i	$0.519227\pi$
$164$	−0.533742	−0.0416782
$165$	−10.2389	−0.797094
$166$	−2.69238	−0.208969
$167$	−3.90535	−0.302205	−0.151103	−	0.988518i	$-0.548282\pi$
$167$	−3.90535	−0.302205	−0.151103	+	0.988518i	$0.548282\pi$
$168$	−16.6069	−1.28125
$169$	19.2319	1.47938
$170$	−18.4032	−1.41146
$171$	18.5437	1.41807
$172$	−0.546558	−0.0416746
$173$	−13.2039	−1.00388	−0.501938	−	0.864904i	$-0.667379\pi$
$173$	−13.2039	−1.00388	−0.501938	+	0.864904i	$0.667379\pi$
$174$	20.3504	1.54276
$175$	−22.3498	−1.68948
$176$	1.00000	0.0753778
$177$	−34.6148	−2.60180
$178$	−11.9330	−0.894418
$179$	−3.67003	−0.274311	−0.137155	−	0.990550i	$-0.543796\pi$
$179$	−3.67003	−0.274311	−0.137155	+	0.990550i	$0.543796\pi$
$180$	24.8202	1.84999
$181$	−10.5861	−0.786856	−0.393428	−	0.919355i	$-0.628711\pi$
$181$	−10.5861	−0.786856	−0.393428	+	0.919355i	$0.628711\pi$
$182$	28.3465	2.10118
$183$	14.6156	1.08042
$184$	−8.31678	−0.613121
$185$	−24.2961	−1.78628
$186$	33.1404	2.42997
$187$	5.97827	0.437174
$188$	6.46522	0.471525
$189$	84.0779	6.11577
$190$	−7.07992	−0.513631
$191$	−10.2997	−0.745257	−0.372629	−	0.927981i	$-0.621543\pi$
$191$	−10.2997	−0.745257	−0.372629	+	0.927981i	$0.621543\pi$
$192$	−3.32608	−0.240039
$193$	−15.1832	−1.09291	−0.546455	−	0.837488i	$-0.684023\pi$
$193$	−15.1832	−1.09291	−0.546455	+	0.837488i	$0.684023\pi$
$194$	14.3699	1.03170
$195$	−58.1293	−4.16272
$196$	17.9295	1.28068
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−8.06282	−0.572999
$199$	−8.03688	−0.569720	−0.284860	−	0.958569i	$-0.591947\pi$
$199$	−8.03688	−0.569720	−0.284860	+	0.958569i	$0.591947\pi$
$200$	−4.47627	−0.316520
$201$	−20.1431	−1.42078
$202$	3.65568	0.257213
$203$	−30.5490	−2.14412
$204$	−19.8842	−1.39217
$205$	−1.64305	−0.114755
$206$	−2.71822	−0.189387
$207$	67.0566	4.66076
$208$	5.67732	0.393651
$209$	2.29990	0.159088
$210$	−51.1221	−3.52776
$211$	−19.7140	−1.35717	−0.678584	−	0.734522i	$-0.737406\pi$
$211$	−19.7140	−1.35717	−0.678584	+	0.734522i	$0.737406\pi$
$212$	0.736628	0.0505918
$213$	−9.79089	−0.670861
$214$	−10.9451	−0.748193
$215$	−1.68250	−0.114746
$216$	16.8393	1.14577
$217$	−49.7487	−3.37716
$218$	2.56588	0.173783
$219$	35.5529	2.40244
$220$	3.07836	0.207543
$221$	33.9405	2.28309
$222$	−26.2513	−1.76187
$223$	−18.4166	−1.23327	−0.616634	−	0.787250i	$-0.711504\pi$
$223$	−18.4166	−1.23327	−0.616634	+	0.787250i	$0.711504\pi$
$224$	4.99294	0.333605
$225$	36.0914	2.40609
$226$	6.00200	0.399247
$227$	16.5122	1.09595	0.547977	−	0.836494i	$-0.315398\pi$
$227$	16.5122	1.09595	0.547977	+	0.836494i	$0.315398\pi$
$228$	−7.64966	−0.506611
$229$	1.49450	0.0987596	0.0493798	−	0.998780i	$-0.484276\pi$
$229$	1.49450	0.0987596	0.0493798	+	0.998780i	$0.484276\pi$
$230$	−25.6020	−1.68815
$231$	16.6069	1.09266
$232$	−6.11844	−0.401695
$233$	20.4656	1.34075	0.670373	−	0.742024i	$-0.266134\pi$
$233$	20.4656	1.34075	0.670373	+	0.742024i	$0.266134\pi$
$234$	−45.7752	−2.99242
$235$	19.9022	1.29828
$236$	10.4071	0.677443
$237$	18.7850	1.22022
$238$	29.8492	1.93483
$239$	27.1703	1.75750	0.878749	−	0.477284i	$-0.158379\pi$
$239$	27.1703	1.75750	0.878749	+	0.477284i	$0.158379\pi$
$240$	−10.2389	−0.660916
$241$	9.24820	0.595729	0.297865	−	0.954608i	$-0.403726\pi$
$241$	9.24820	0.595729	0.297865	+	0.954608i	$0.403726\pi$
$242$	−1.00000	−0.0642824
$243$	−55.3198	−3.54877
$244$	−4.39424	−0.281312
$245$	55.1934	3.52618
$246$	−1.77527	−0.113187
$247$	13.0573	0.830814
$248$	−9.96380	−0.632702
$249$	−8.95507	−0.567505
$250$	1.61222	0.101966
$251$	22.4348	1.41607	0.708037	−	0.706176i	$-0.249581\pi$
$251$	22.4348	1.41607	0.708037	+	0.706176i	$0.249581\pi$
$252$	−40.2572	−2.53597
$253$	8.31678	0.522871
$254$	5.12157	0.321356
$255$	−61.2106	−3.83316
$256$	1.00000	0.0625000
$257$	−0.609278	−0.0380057	−0.0190029	−	0.999819i	$-0.506049\pi$
$257$	−0.609278	−0.0380057	−0.0190029	+	0.999819i	$0.506049\pi$
$258$	−1.81790	−0.113177
$259$	39.4071	2.44864
$260$	17.4768	1.08387
$261$	49.3318	3.05356
$262$	16.7004	1.03175
$263$	11.4949	0.708805	0.354402	−	0.935093i	$-0.384684\pi$
$263$	11.4949	0.708805	0.354402	+	0.935093i	$0.384684\pi$
$264$	3.32608	0.204706
$265$	2.26760	0.139298
$266$	11.4833	0.704085
$267$	−39.6902	−2.42900
$268$	6.05610	0.369935
$269$	13.1319	0.800666	0.400333	−	0.916370i	$-0.368894\pi$
$269$	13.1319	0.800666	0.400333	+	0.916370i	$0.368894\pi$
$270$	51.8375	3.15473
$271$	−12.0642	−0.732847	−0.366423	−	0.930448i	$-0.619418\pi$
$271$	−12.0642	−0.732847	−0.366423	+	0.930448i	$0.619418\pi$
$272$	5.97827	0.362486
$273$	94.2829	5.70626
$274$	−0.0565638	−0.00341715
$275$	4.47627	0.269929
$276$	−27.6623	−1.66507
$277$	23.3768	1.40457	0.702287	−	0.711894i	$-0.252163\pi$
$277$	23.3768	1.40457	0.702287	+	0.711894i	$0.252163\pi$
$278$	12.9949	0.779384
$279$	80.3363	4.80961
$280$	15.3701	0.918537
$281$	−12.0736	−0.720253	−0.360127	−	0.932903i	$-0.617267\pi$
$281$	−12.0736	−0.720253	−0.360127	+	0.932903i	$0.617267\pi$
$282$	21.5038	1.28054
$283$	−13.1759	−0.783224	−0.391612	−	0.920130i	$-0.628083\pi$
$283$	−13.1759	−0.783224	−0.391612	+	0.920130i	$0.628083\pi$
$284$	2.94367	0.174675
$285$	−23.5484	−1.39489
$286$	−5.67732	−0.335707
$287$	2.66494	0.157307
$288$	−8.06282	−0.475106
$289$	18.7397	1.10233
$290$	−18.8347	−1.10601
$291$	47.7953	2.80181
$292$	−10.6891	−0.625534
$293$	−10.8293	−0.632656	−0.316328	−	0.948650i	$-0.602450\pi$
$293$	−10.8293	−0.632656	−0.316328	+	0.948650i	$0.602450\pi$
$294$	59.6350	3.47798
$295$	32.0367	1.86525
$296$	7.89255	0.458745
$297$	−16.8393	−0.977118
$298$	−14.2046	−0.822848
$299$	47.2170	2.73063
$300$	−14.8884	−0.859585
$301$	2.72893	0.157293
$302$	−15.6989	−0.903372
$303$	12.1591	0.698521
$304$	2.29990	0.131908
$305$	−13.5270	−0.774556
$306$	−48.2017	−2.75551
$307$	5.10910	0.291592	0.145796	−	0.989315i	$-0.453426\pi$
$307$	5.10910	0.291592	0.145796	+	0.989315i	$0.453426\pi$
$308$	−4.99294	−0.284499
$309$	−9.04102	−0.514325
$310$	−30.6721	−1.74206
$311$	7.90428	0.448210	0.224105	−	0.974565i	$-0.428054\pi$
$311$	7.90428	0.448210	0.224105	+	0.974565i	$0.428054\pi$
$312$	18.8832	1.06905
$313$	−24.4602	−1.38257	−0.691287	−	0.722580i	$-0.742956\pi$
$313$	−24.4602	−1.38257	−0.691287	+	0.722580i	$0.742956\pi$
$314$	6.70996	0.378665
$315$	−123.926	−6.98244
$316$	−5.64779	−0.317713
$317$	9.52013	0.534704	0.267352	−	0.963599i	$-0.413851\pi$
$317$	9.52013	0.534704	0.267352	+	0.963599i	$0.413851\pi$
$318$	2.45009	0.137394
$319$	6.11844	0.342567
$320$	3.07836	0.172085
$321$	−36.4044	−2.03189
$322$	41.5252	2.31411
$323$	13.7494	0.765039
$324$	31.8206	1.76781
$325$	25.4132	1.40967
$326$	1.54140	0.0853702
$327$	8.53431	0.471949
$328$	0.533742	0.0294709
$329$	−32.2805	−1.77968
$330$	10.2389	0.563631
$331$	−5.62003	−0.308905	−0.154453	−	0.988000i	$-0.549361\pi$
$331$	−5.62003	−0.308905	−0.154453	+	0.988000i	$0.549361\pi$
$332$	2.69238	0.147763
$333$	−63.6362	−3.48724
$334$	3.90535	0.213691
$335$	18.6428	1.01857
$336$	16.6069	0.905983
$337$	4.35482	0.237222	0.118611	−	0.992941i	$-0.462156\pi$
$337$	4.35482	0.237222	0.118611	+	0.992941i	$0.462156\pi$
$338$	−19.2319	−1.04608
$339$	19.9631	1.08425
$340$	18.4032	0.998055
$341$	9.96380	0.539570
$342$	−18.5437	−1.00273
$343$	−54.5704	−2.94652
$344$	0.546558	0.0294684
$345$	−85.1543	−4.58455
$346$	13.2039	0.709847
$347$	−5.96140	−0.320025	−0.160012	−	0.987115i	$-0.551153\pi$
$347$	−5.96140	−0.320025	−0.160012	+	0.987115i	$0.551153\pi$
$348$	−20.3504	−1.09090
$349$	16.4562	0.880880	0.440440	−	0.897782i	$-0.354822\pi$
$349$	16.4562	0.880880	0.440440	+	0.897782i	$0.354822\pi$
$350$	22.3498	1.19465
$351$	−95.6023	−5.10287
$352$	−1.00000	−0.0533002
$353$	19.2799	1.02616	0.513081	−	0.858340i	$-0.328504\pi$
$353$	19.2799	1.02616	0.513081	+	0.858340i	$0.328504\pi$
$354$	34.6148	1.83975
$355$	9.06167	0.480944
$356$	11.9330	0.632449
$357$	99.2807	5.25449
$358$	3.67003	0.193967
$359$	−24.1912	−1.27676	−0.638381	−	0.769721i	$-0.720396\pi$
$359$	−24.1912	−1.27676	−0.638381	+	0.769721i	$0.720396\pi$
$360$	−24.8202	−1.30814
$361$	−13.7105	−0.721603
$362$	10.5861	0.556391
$363$	−3.32608	−0.174574
$364$	−28.3465	−1.48576
$365$	−32.9050	−1.72232
$366$	−14.6156	−0.763970
$367$	8.81399	0.460087	0.230043	−	0.973180i	$-0.426113\pi$
$367$	8.81399	0.460087	0.230043	+	0.973180i	$0.426113\pi$
$368$	8.31678	0.433542
$369$	−4.30346	−0.224029
$370$	24.2961	1.26309
$371$	−3.67794	−0.190949
$372$	−33.1404	−1.71825
$373$	19.7299	1.02158	0.510788	−	0.859707i	$-0.329354\pi$
$373$	19.7299	1.02158	0.510788	+	0.859707i	$0.329354\pi$
$374$	−5.97827	−0.309129
$375$	5.36237	0.276912
$376$	−6.46522	−0.333418
$377$	34.7363	1.78901
$378$	−84.0779	−4.32450
$379$	−0.937742	−0.0481686	−0.0240843	−	0.999710i	$-0.507667\pi$
$379$	−0.937742	−0.0481686	−0.0240843	+	0.999710i	$0.507667\pi$
$380$	7.07992	0.363192
$381$	17.0348	0.872717
$382$	10.2997	0.526976
$383$	−2.98573	−0.152564	−0.0762819	−	0.997086i	$-0.524305\pi$
$383$	−2.98573	−0.152564	−0.0762819	+	0.997086i	$0.524305\pi$
$384$	3.32608	0.169733
$385$	−15.3701	−0.783331
$386$	15.1832	0.772804
$387$	−4.40680	−0.224010
$388$	−14.3699	−0.729519
$389$	16.3564	0.829305	0.414652	−	0.909980i	$-0.363903\pi$
$389$	16.3564	0.829305	0.414652	+	0.909980i	$0.363903\pi$
$390$	58.1293	2.94349
$391$	49.7199	2.51444
$392$	−17.9295	−0.905576
$393$	55.5468	2.80197
$394$	1.00000	0.0503793
$395$	−17.3859	−0.874780
$396$	8.06282	0.405172
$397$	17.8624	0.896487	0.448244	−	0.893911i	$-0.352050\pi$
$397$	17.8624	0.896487	0.448244	+	0.893911i	$0.352050\pi$
$398$	8.03688	0.402853
$399$	38.1943	1.91211
$400$	4.47627	0.223814
$401$	−20.0472	−1.00111	−0.500554	−	0.865705i	$-0.666870\pi$
$401$	−20.0472	−1.00111	−0.500554	+	0.865705i	$0.666870\pi$
$402$	20.1431	1.00465
$403$	56.5676	2.81784
$404$	−3.65568	−0.181877
$405$	97.9550	4.86742
$406$	30.5490	1.51612
$407$	−7.89255	−0.391219
$408$	19.8842	0.984415
$409$	−7.76545	−0.383977	−0.191988	−	0.981397i	$-0.561494\pi$
$409$	−7.76545	−0.383977	−0.191988	+	0.981397i	$0.561494\pi$
$410$	1.64305	0.0811443
$411$	−0.188136	−0.00928006
$412$	2.71822	0.133917
$413$	−51.9619	−2.55688
$414$	−67.0566	−3.29565
$415$	8.28810	0.406847
$416$	−5.67732	−0.278353
$417$	43.2222	2.11660
$418$	−2.29990	−0.112492
$419$	−14.8554	−0.725733	−0.362867	−	0.931841i	$-0.618202\pi$
$419$	−14.8554	−0.725733	−0.362867	+	0.931841i	$0.618202\pi$
$420$	51.1221	2.49450
$421$	13.9742	0.681063	0.340531	−	0.940233i	$-0.389393\pi$
$421$	13.9742	0.681063	0.340531	+	0.940233i	$0.389393\pi$
$422$	19.7140	0.959663
$423$	52.1279	2.53454
$424$	−0.736628	−0.0357738
$425$	26.7604	1.29807
$426$	9.79089	0.474370
$427$	21.9402	1.06176
$428$	10.9451	0.529052
$429$	−18.8832	−0.911690
$430$	1.68250	0.0811373
$431$	−24.0391	−1.15792	−0.578962	−	0.815355i	$-0.696542\pi$
$431$	−24.0391	−1.15792	−0.578962	+	0.815355i	$0.696542\pi$
$432$	−16.8393	−0.810183
$433$	29.3760	1.41172	0.705860	−	0.708352i	$-0.250561\pi$
$433$	29.3760	1.41172	0.705860	+	0.708352i	$0.250561\pi$
$434$	49.7487	2.38801
$435$	−62.6458	−3.00364
$436$	−2.56588	−0.122883
$437$	19.1278	0.915005
$438$	−35.5529	−1.69878
$439$	−18.4316	−0.879691	−0.439846	−	0.898073i	$-0.644967\pi$
$439$	−18.4316	−0.879691	−0.439846	+	0.898073i	$0.644967\pi$
$440$	−3.07836	−0.146755
$441$	144.562	6.88392
$442$	−33.9405	−1.61439
$443$	−14.1536	−0.672457	−0.336228	−	0.941781i	$-0.609151\pi$
$443$	−14.1536	−0.672457	−0.336228	+	0.941781i	$0.609151\pi$
$444$	26.2513	1.24583
$445$	36.7341	1.74136
$446$	18.4166	0.872052
$447$	−47.2455	−2.23464
$448$	−4.99294	−0.235894
$449$	8.15896	0.385045	0.192523	−	0.981293i	$-0.438333\pi$
$449$	8.15896	0.385045	0.192523	+	0.981293i	$0.438333\pi$
$450$	−36.0914	−1.70136
$451$	−0.533742	−0.0251329
$452$	−6.00200	−0.282310
$453$	−52.2159	−2.45332
$454$	−16.5122	−0.774956
$455$	−87.2607	−4.09084
$456$	7.64966	0.358228
$457$	−22.5384	−1.05430	−0.527152	−	0.849771i	$-0.676740\pi$
$457$	−22.5384	−1.05430	−0.527152	+	0.849771i	$0.676740\pi$
$458$	−1.49450	−0.0698336
$459$	−100.670	−4.69888
$460$	25.6020	1.19370
$461$	−6.70832	−0.312438	−0.156219	−	0.987722i	$-0.549931\pi$
$461$	−6.70832	−0.312438	−0.156219	+	0.987722i	$0.549931\pi$
$462$	−16.6069	−0.772625
$463$	−0.00136530	−6.34510e−5 0	−3.17255e−5	−	1.00000i	$-0.500010\pi$
$463$	−0.00136530	−6.34510e−5 0	−3.17255e−5		1.00000i	$0.500010\pi$
$464$	6.11844	0.284041
$465$	−102.018	−4.73097
$466$	−20.4656	−0.948050
$467$	6.43527	0.297789	0.148894	−	0.988853i	$-0.452429\pi$
$467$	6.43527	0.297789	0.148894	+	0.988853i	$0.452429\pi$
$468$	45.7752	2.11596
$469$	−30.2378	−1.39625
$470$	−19.9022	−0.918022
$471$	22.3179	1.02835
$472$	−10.4071	−0.479024
$473$	−0.546558	−0.0251308
$474$	−18.7850	−0.862825
$475$	10.2950	0.472366
$476$	−29.8492	−1.36813
$477$	5.93930	0.271942
$478$	−27.1703	−1.24274
$479$	2.52588	0.115410	0.0577052	−	0.998334i	$-0.481622\pi$
$479$	2.52588	0.115410	0.0577052	+	0.998334i	$0.481622\pi$
$480$	10.2389	0.467338
$481$	−44.8085	−2.04309
$482$	−9.24820	−0.421244
$483$	138.116	6.28451
$484$	1.00000	0.0454545
$485$	−44.2355	−2.00863
$486$	55.3198	2.50936
$487$	−7.56628	−0.342861	−0.171431	−	0.985196i	$-0.554839\pi$
$487$	−7.56628	−0.342861	−0.171431	+	0.985196i	$0.554839\pi$
$488$	4.39424	0.198918
$489$	5.12682	0.231843
$490$	−55.1934	−2.49338
$491$	−13.7731	−0.621574	−0.310787	−	0.950480i	$-0.600593\pi$
$491$	−13.7731	−0.621574	−0.310787	+	0.950480i	$0.600593\pi$
$492$	1.77527	0.0800353
$493$	36.5777	1.64737
$494$	−13.0573	−0.587474
$495$	24.8202	1.11559
$496$	9.96380	0.447388
$497$	−14.6976	−0.659277
$498$	8.95507	0.401286
$499$	20.5814	0.921349	0.460674	−	0.887569i	$-0.347608\pi$
$499$	20.5814	0.921349	0.460674	+	0.887569i	$0.347608\pi$
$500$	−1.61222	−0.0721006
$501$	12.9895	0.580329
$502$	−22.4348	−1.00131
$503$	42.5398	1.89675	0.948377	−	0.317145i	$-0.102724\pi$
$503$	42.5398	1.89675	0.948377	+	0.317145i	$0.102724\pi$
$504$	40.2572	1.79320
$505$	−11.2535	−0.500773
$506$	−8.31678	−0.369726
$507$	−63.9670	−2.84087
$508$	−5.12157	−0.227233
$509$	−34.8019	−1.54257	−0.771283	−	0.636493i	$-0.780385\pi$
$509$	−34.8019	−1.54257	−0.771283	+	0.636493i	$0.780385\pi$
$510$	61.2106	2.71045
$511$	53.3703	2.36096
$512$	−1.00000	−0.0441942
$513$	−38.7288	−1.70992
$514$	0.609278	0.0268741
$515$	8.36764	0.368722
$516$	1.81790	0.0800284
$517$	6.46522	0.284340
$518$	−39.4071	−1.73145
$519$	43.9173	1.92776
$520$	−17.4768	−0.766408
$521$	−21.5008	−0.941968	−0.470984	−	0.882142i	$-0.656101\pi$
$521$	−21.5008	−0.941968	−0.470984	+	0.882142i	$0.656101\pi$
$522$	−49.3318	−2.15920
$523$	11.4735	0.501702	0.250851	−	0.968026i	$-0.419290\pi$
$523$	11.4735	0.501702	0.250851	+	0.968026i	$0.419290\pi$
$524$	−16.7004	−0.729560
$525$	74.3372	3.24434
$526$	−11.4949	−0.501201
$527$	59.5663	2.59475
$528$	−3.32608	−0.144749
$529$	46.1688	2.00734
$530$	−2.26760	−0.0984984
$531$	83.9103	3.64140
$532$	−11.4833	−0.497864
$533$	−3.03022	−0.131253
$534$	39.6902	1.71756
$535$	33.6930	1.45667
$536$	−6.05610	−0.261584
$537$	12.2068	0.526763
$538$	−13.1319	−0.566156
$539$	17.9295	0.772278
$540$	−51.8375	−2.23073
$541$	34.9383	1.50211	0.751057	−	0.660237i	$-0.229544\pi$
$541$	34.9383	1.50211	0.751057	+	0.660237i	$0.229544\pi$
$542$	12.0642	0.518201
$543$	35.2101	1.51101
$544$	−5.97827	−0.256316
$545$	−7.89868	−0.338342
$546$	−94.2829	−4.03493
$547$	−38.5803	−1.64958	−0.824788	−	0.565442i	$-0.808705\pi$
$547$	−38.5803	−1.64958	−0.824788	+	0.565442i	$0.808705\pi$
$548$	0.0565638	0.00241629
$549$	−35.4299	−1.51211
$550$	−4.47627	−0.190869
$551$	14.0718	0.599479
$552$	27.6623	1.17738
$553$	28.1991	1.19915
$554$	−23.3768	−0.993183
$555$	80.8107	3.43022
$556$	−12.9949	−0.551108
$557$	−32.9779	−1.39732	−0.698658	−	0.715455i	$-0.746219\pi$
$557$	−32.9779	−1.39732	−0.698658	+	0.715455i	$0.746219\pi$
$558$	−80.3363	−3.40091
$559$	−3.10298	−0.131242
$560$	−15.3701	−0.649504
$561$	−19.8842	−0.839512
$562$	12.0736	0.509296
$563$	−15.3290	−0.646040	−0.323020	−	0.946392i	$-0.604698\pi$
$563$	−15.3290	−0.646040	−0.323020	+	0.946392i	$0.604698\pi$
$564$	−21.5038	−0.905475
$565$	−18.4763	−0.777303
$566$	13.1759	0.553823
$567$	−158.878	−6.67226
$568$	−2.94367	−0.123514
$569$	−22.2848	−0.934226	−0.467113	−	0.884198i	$-0.654706\pi$
$569$	−22.2848	−0.934226	−0.467113	+	0.884198i	$0.654706\pi$
$570$	23.5484	0.986333
$571$	11.7029	0.489751	0.244876	−	0.969555i	$-0.421253\pi$
$571$	11.7029	0.489751	0.244876	+	0.969555i	$0.421253\pi$
$572$	5.67732	0.237381
$573$	34.2575	1.43113
$574$	−2.66494	−0.111233
$575$	37.2282	1.55252
$576$	8.06282	0.335951
$577$	−13.7119	−0.570834	−0.285417	−	0.958403i	$-0.592132\pi$
$577$	−13.7119	−0.570834	−0.285417	+	0.958403i	$0.592132\pi$
$578$	−18.7397	−0.779468
$579$	50.5005	2.09873
$580$	18.8347	0.782069
$581$	−13.4429	−0.557705
$582$	−47.7953	−1.98118
$583$	0.736628	0.0305080
$584$	10.6891	0.442320
$585$	140.912	5.82600
$586$	10.8293	0.447355
$587$	35.8085	1.47797	0.738987	−	0.673720i	$-0.235304\pi$
$587$	35.8085	1.47797	0.738987	+	0.673720i	$0.235304\pi$
$588$	−59.6350	−2.45930
$589$	22.9158	0.944228
$590$	−32.0367	−1.31893
$591$	3.32608	0.136817
$592$	−7.89255	−0.324382
$593$	10.9508	0.449694	0.224847	−	0.974394i	$-0.427812\pi$
$593$	10.9508	0.449694	0.224847	+	0.974394i	$0.427812\pi$
$594$	16.8393	0.690927
$595$	−91.8863	−3.76697
$596$	14.2046	0.581841
$597$	26.7313	1.09404
$598$	−47.2170	−1.93085
$599$	−30.8002	−1.25846	−0.629232	−	0.777218i	$-0.716630\pi$
$599$	−30.8002	−1.25846	−0.629232	+	0.777218i	$0.716630\pi$
$600$	14.8884	0.607818
$601$	−8.23544	−0.335931	−0.167965	−	0.985793i	$-0.553720\pi$
$601$	−8.23544	−0.335931	−0.167965	+	0.985793i	$0.553720\pi$
$602$	−2.72893	−0.111223
$603$	48.8292	1.98848
$604$	15.6989	0.638780
$605$	3.07836	0.125153
$606$	−12.1591	−0.493929
$607$	−18.3201	−0.743592	−0.371796	−	0.928315i	$-0.621258\pi$
$607$	−18.3201	−0.743592	−0.371796	+	0.928315i	$0.621258\pi$
$608$	−2.29990	−0.0932733
$609$	101.609	4.11739
$610$	13.5270	0.547693
$611$	36.7051	1.48493
$612$	48.2017	1.94844
$613$	−21.7302	−0.877673	−0.438836	−	0.898567i	$-0.644609\pi$
$613$	−21.7302	−0.877673	−0.438836	+	0.898567i	$0.644609\pi$
$614$	−5.10910	−0.206187
$615$	5.46491	0.220366
$616$	4.99294	0.201171
$617$	26.8217	1.07980	0.539901	−	0.841728i	$-0.318461\pi$
$617$	26.8217	1.07980	0.539901	+	0.841728i	$0.318461\pi$
$618$	9.04102	0.363683
$619$	3.65664	0.146973	0.0734863	−	0.997296i	$-0.476587\pi$
$619$	3.65664	0.146973	0.0734863	+	0.997296i	$0.476587\pi$
$620$	30.6721	1.23182
$621$	−140.049	−5.61997
$622$	−7.90428	−0.316933
$623$	−59.5809	−2.38706
$624$	−18.8832	−0.755934
$625$	−27.3443	−1.09377
$626$	24.4602	0.977628
$627$	−7.64966	−0.305498
$628$	−6.70996	−0.267757
$629$	−47.1838	−1.88134
$630$	123.926	4.93733
$631$	20.9236	0.832954	0.416477	−	0.909146i	$-0.363265\pi$
$631$	20.9236	0.832954	0.416477	+	0.909146i	$0.363265\pi$
$632$	5.64779	0.224657
$633$	65.5704	2.60619
$634$	−9.52013	−0.378093
$635$	−15.7660	−0.625655
$636$	−2.45009	−0.0971522
$637$	101.791	4.03312
$638$	−6.11844	−0.242231
$639$	23.7343	0.938914
$640$	−3.07836	−0.121683
$641$	14.4841	0.572086	0.286043	−	0.958217i	$-0.407660\pi$
$641$	14.4841	0.572086	0.286043	+	0.958217i	$0.407660\pi$
$642$	36.4044	1.43677
$643$	9.10502	0.359067	0.179533	−	0.983752i	$-0.442541\pi$
$643$	9.10502	0.359067	0.179533	+	0.983752i	$0.442541\pi$
$644$	−41.5252	−1.63632
$645$	5.59613	0.220347
$646$	−13.7494	−0.540964
$647$	−38.3614	−1.50814	−0.754071	−	0.656793i	$-0.771913\pi$
$647$	−38.3614	−1.50814	−0.754071	+	0.656793i	$0.771913\pi$
$648$	−31.8206	−1.25003
$649$	10.4071	0.408513
$650$	−25.4132	−0.996788
$651$	165.468	6.48521
$652$	−1.54140	−0.0603658
$653$	−9.44799	−0.369728	−0.184864	−	0.982764i	$-0.559185\pi$
$653$	−9.44799	−0.369728	−0.184864	+	0.982764i	$0.559185\pi$
$654$	−8.53431	−0.333718
$655$	−51.4097	−2.00874
$656$	−0.533742	−0.0208391
$657$	−86.1845	−3.36238
$658$	32.2805	1.25842
$659$	4.61526	0.179785	0.0898925	−	0.995951i	$-0.471348\pi$
$659$	4.61526	0.179785	0.0898925	+	0.995951i	$0.471348\pi$
$660$	−10.2389	−0.398547
$661$	−41.5458	−1.61594	−0.807972	−	0.589220i	$-0.799435\pi$
$661$	−41.5458	−1.61594	−0.807972	+	0.589220i	$0.799435\pi$
$662$	5.62003	0.218429
$663$	−112.889	−4.38424
$664$	−2.69238	−0.104485
$665$	−35.3496	−1.37080
$666$	63.6362	2.46585
$667$	50.8857	1.97030
$668$	−3.90535	−0.151103
$669$	61.2552	2.36826
$670$	−18.6428	−0.720235
$671$	−4.39424	−0.169638
$672$	−16.6069	−0.640627
$673$	40.5745	1.56403	0.782017	−	0.623257i	$-0.214191\pi$
$673$	40.5745	1.56403	0.782017	+	0.623257i	$0.214191\pi$
$674$	−4.35482	−0.167742
$675$	−75.3775	−2.90128
$676$	19.2319	0.739690
$677$	−30.2658	−1.16321	−0.581605	−	0.813472i	$-0.697575\pi$
$677$	−30.2658	−1.16321	−0.581605	+	0.813472i	$0.697575\pi$
$678$	−19.9631	−0.766680
$679$	71.7479	2.75343
$680$	−18.4032	−0.705732
$681$	−54.9209	−2.10458
$682$	−9.96380	−0.381534
$683$	−34.8576	−1.33379	−0.666894	−	0.745153i	$-0.732377\pi$
$683$	−34.8576	−1.33379	−0.666894	+	0.745153i	$0.732377\pi$
$684$	18.5437	0.709036
$685$	0.174124	0.00665292
$686$	54.5704	2.08351
$687$	−4.97084	−0.189649
$688$	−0.546558	−0.0208373
$689$	4.18207	0.159324
$690$	85.1543	3.24177
$691$	13.1681	0.500937	0.250469	−	0.968125i	$-0.419415\pi$
$691$	13.1681	0.500937	0.250469	+	0.968125i	$0.419415\pi$
$692$	−13.2039	−0.501938
$693$	−40.2572	−1.52924
$694$	5.96140	0.226292
$695$	−40.0030	−1.51740
$696$	20.3504	0.771381
$697$	−3.19085	−0.120862
$698$	−16.4562	−0.622876
$699$	−68.0702	−2.57465
$700$	−22.3498	−0.844742
$701$	16.7049	0.630934	0.315467	−	0.948937i	$-0.397839\pi$
$701$	16.7049	0.630934	0.315467	+	0.948937i	$0.397839\pi$
$702$	95.6023	3.60828
$703$	−18.1521	−0.684619
$704$	1.00000	0.0376889
$705$	−66.1965	−2.49310
$706$	−19.2799	−0.725607
$707$	18.2526	0.686460
$708$	−34.6148	−1.30090
$709$	−18.5079	−0.695080	−0.347540	−	0.937665i	$-0.612983\pi$
$709$	−18.5079	−0.695080	−0.347540	+	0.937665i	$0.612983\pi$
$710$	−9.06167	−0.340078
$711$	−45.5371	−1.70778
$712$	−11.9330	−0.447209
$713$	82.8667	3.10338
$714$	−99.2807	−3.71549
$715$	17.4768	0.653595
$716$	−3.67003	−0.137155
$717$	−90.3705	−3.37495
$718$	24.1912	0.902807
$719$	23.0547	0.859796	0.429898	−	0.902878i	$-0.358550\pi$
$719$	23.0547	0.859796	0.429898	+	0.902878i	$0.358550\pi$
$720$	24.8202	0.924995
$721$	−13.5719	−0.505444
$722$	13.7105	0.510250
$723$	−30.7603	−1.14399
$724$	−10.5861	−0.393428
$725$	27.3878	1.01716
$726$	3.32608	0.123442
$727$	20.3931	0.756338	0.378169	−	0.925736i	$-0.376554\pi$
$727$	20.3931	0.756338	0.378169	+	0.925736i	$0.376554\pi$
$728$	28.3465	1.05059
$729$	88.5364	3.27913
$730$	32.9050	1.21787
$731$	−3.26747	−0.120852
$732$	14.6156	0.540208
$733$	−45.7363	−1.68931	−0.844654	−	0.535313i	$-0.820194\pi$
$733$	−45.7363	−1.68931	−0.844654	+	0.535313i	$0.820194\pi$
$734$	−8.81399	−0.325330
$735$	−183.578	−6.77136
$736$	−8.31678	−0.306560
$737$	6.05610	0.223079
$738$	4.30346	0.158413
$739$	−42.4795	−1.56264	−0.781318	−	0.624134i	$-0.785452\pi$
$739$	−42.4795	−1.56264	−0.781318	+	0.624134i	$0.785452\pi$
$740$	−24.2961	−0.893142
$741$	−43.4296	−1.59542
$742$	3.67794	0.135022
$743$	7.20331	0.264264	0.132132	−	0.991232i	$-0.457818\pi$
$743$	7.20331	0.264264	0.132132	+	0.991232i	$0.457818\pi$
$744$	33.1404	1.21499
$745$	43.7267	1.60202
$746$	−19.7299	−0.722364
$747$	21.7082	0.794260
$748$	5.97827	0.218587
$749$	−54.6484	−1.99681
$750$	−5.36237	−0.195806
$751$	44.5265	1.62479	0.812397	−	0.583105i	$-0.198162\pi$
$751$	44.5265	1.62479	0.812397	+	0.583105i	$0.198162\pi$
$752$	6.46522	0.235762
$753$	−74.6200	−2.71930
$754$	−34.7363	−1.26502
$755$	48.3269	1.75880
$756$	84.0779	3.05788
$757$	−18.8720	−0.685914	−0.342957	−	0.939351i	$-0.611429\pi$
$757$	−18.8720	−0.685914	−0.342957	+	0.939351i	$0.611429\pi$
$758$	0.937742	0.0340603
$759$	−27.6623	−1.00408
$760$	−7.07992	−0.256816
$761$	1.35454	0.0491021	0.0245511	−	0.999699i	$-0.492184\pi$
$761$	1.35454	0.0491021	0.0245511	+	0.999699i	$0.492184\pi$
$762$	−17.0348	−0.617104
$763$	12.8113	0.463799
$764$	−10.2997	−0.372629
$765$	148.382	5.36476
$766$	2.98573	0.107879
$767$	59.0842	2.13341
$768$	−3.32608	−0.120020
$769$	15.1714	0.547094	0.273547	−	0.961859i	$-0.411803\pi$
$769$	15.1714	0.547094	0.273547	+	0.961859i	$0.411803\pi$
$770$	15.3701	0.553898
$771$	2.02651	0.0729829
$772$	−15.1832	−0.546455
$773$	12.0276	0.432604	0.216302	−	0.976326i	$-0.430600\pi$
$773$	12.0276	0.432604	0.216302	+	0.976326i	$0.430600\pi$
$774$	4.40680	0.158399
$775$	44.6007	1.60210
$776$	14.3699	0.515848
$777$	−131.071	−4.70215
$778$	−16.3564	−0.586407
$779$	−1.22755	−0.0439817
$780$	−58.1293	−2.08136
$781$	2.94367	0.105333
$782$	−49.7199	−1.77798
$783$	−103.030	−3.68201
$784$	17.9295	0.640339
$785$	−20.6556	−0.737232
$786$	−55.5468	−1.98129
$787$	35.2192	1.25543	0.627714	−	0.778444i	$-0.283991\pi$
$787$	35.2192	1.25543	0.627714	+	0.778444i	$0.283991\pi$
$788$	−1.00000	−0.0356235
$789$	−38.2329	−1.36113
$790$	17.3859	0.618563
$791$	29.9677	1.06553
$792$	−8.06282	−0.286500
$793$	−24.9475	−0.885911
$794$	−17.8624	−0.633912
$795$	−7.54223	−0.267495
$796$	−8.03688	−0.284860
$797$	−1.32566	−0.0469572	−0.0234786	−	0.999724i	$-0.507474\pi$
$797$	−1.32566	−0.0469572	−0.0234786	+	0.999724i	$0.507474\pi$
$798$	−38.1943	−1.35206
$799$	38.6508	1.36737
$800$	−4.47627	−0.158260
$801$	96.2138	3.39955
$802$	20.0472	0.707890
$803$	−10.6891	−0.377211
$804$	−20.1431	−0.710391
$805$	−127.829	−4.50539
$806$	−56.5676	−1.99251
$807$	−43.6778	−1.53753
$808$	3.65568	0.128606
$809$	−37.2982	−1.31133	−0.655667	−	0.755050i	$-0.727612\pi$
$809$	−37.2982	−1.31133	−0.655667	+	0.755050i	$0.727612\pi$
$810$	−97.9550	−3.44179
$811$	−10.5223	−0.369489	−0.184744	−	0.982787i	$-0.559146\pi$
$811$	−10.5223	−0.369489	−0.184744	+	0.982787i	$0.559146\pi$
$812$	−30.5490	−1.07206
$813$	40.1264	1.40730
$814$	7.89255	0.276634
$815$	−4.74497	−0.166209
$816$	−19.8842	−0.696086
$817$	−1.25703	−0.0439779
$818$	7.76545	0.271513
$819$	−228.553	−7.98628
$820$	−1.64305	−0.0573777
$821$	−39.1269	−1.36554	−0.682768	−	0.730635i	$-0.739224\pi$
$821$	−39.1269	−1.36554	−0.682768	+	0.730635i	$0.739224\pi$
$822$	0.188136	0.00656199
$823$	15.7365	0.548540	0.274270	−	0.961653i	$-0.411564\pi$
$823$	15.7365	0.548540	0.274270	+	0.961653i	$0.411564\pi$
$824$	−2.71822	−0.0946936
$825$	−14.8884	−0.518349
$826$	51.9619	1.80799
$827$	−41.5515	−1.44489	−0.722444	−	0.691429i	$-0.756981\pi$
$827$	−41.5515	−1.44489	−0.722444	+	0.691429i	$0.756981\pi$
$828$	67.0566	2.33038
$829$	3.65809	0.127051	0.0635254	−	0.997980i	$-0.479766\pi$
$829$	3.65809	0.127051	0.0635254	+	0.997980i	$0.479766\pi$
$830$	−8.28810	−0.287684
$831$	−77.7530	−2.69722
$832$	5.67732	0.196826
$833$	107.187	3.71382
$834$	−43.2222	−1.49666
$835$	−12.0221	−0.416041
$836$	2.29990	0.0795438
$837$	−167.784	−5.79946
$838$	14.8554	0.513171
$839$	20.8373	0.719383	0.359692	−	0.933071i	$-0.382882\pi$
$839$	20.8373	0.719383	0.359692	+	0.933071i	$0.382882\pi$
$840$	−51.1221	−1.76388
$841$	8.43528	0.290872
$842$	−13.9742	−0.481584
$843$	40.1579	1.38311
$844$	−19.7140	−0.678584
$845$	59.2027	2.03664
$846$	−52.1279	−1.79219
$847$	−4.99294	−0.171560
$848$	0.736628	0.0252959
$849$	43.8240	1.50404
$850$	−26.7604	−0.917873
$851$	−65.6406	−2.25013
$852$	−9.79089	−0.335431
$853$	3.05410	0.104570	0.0522851	−	0.998632i	$-0.483350\pi$
$853$	3.05410	0.104570	0.0522851	+	0.998632i	$0.483350\pi$
$854$	−21.9402	−0.750778
$855$	57.0841	1.95223
$856$	−10.9451	−0.374097
$857$	−38.2356	−1.30610	−0.653051	−	0.757314i	$-0.726511\pi$
$857$	−38.2356	−1.30610	−0.653051	+	0.757314i	$0.726511\pi$
$858$	18.8832	0.644662
$859$	−8.70050	−0.296857	−0.148429	−	0.988923i	$-0.547422\pi$
$859$	−8.70050	−0.296857	−0.148429	+	0.988923i	$0.547422\pi$
$860$	−1.68250	−0.0573728
$861$	−8.86381	−0.302078
$862$	24.0391	0.818776
$863$	−54.0101	−1.83852	−0.919262	−	0.393645i	$-0.871214\pi$
$863$	−54.0101	−1.83852	−0.919262	+	0.393645i	$0.871214\pi$
$864$	16.8393	0.572886
$865$	−40.6464	−1.38202
$866$	−29.3760	−0.998236
$867$	−62.3297	−2.11683
$868$	−49.7487	−1.68858
$869$	−5.64779	−0.191588
$870$	62.6458	2.12389
$871$	34.3824	1.16500
$872$	2.56588	0.0868915
$873$	−115.862	−3.92132
$874$	−19.1278	−0.647007
$875$	8.04972	0.272130
$876$	35.5529	1.20122
$877$	−7.87798	−0.266020	−0.133010	−	0.991115i	$-0.542464\pi$
$877$	−7.87798	−0.266020	−0.133010	+	0.991115i	$0.542464\pi$
$878$	18.4316	0.622036
$879$	36.0192	1.21490
$880$	3.07836	0.103771
$881$	20.3535	0.685727	0.342864	−	0.939385i	$-0.388603\pi$
$881$	20.3535	0.685727	0.342864	+	0.939385i	$0.388603\pi$
$882$	−144.562	−4.86766
$883$	−24.0259	−0.808536	−0.404268	−	0.914641i	$-0.632474\pi$
$883$	−24.0259	−0.808536	−0.404268	+	0.914641i	$0.632474\pi$
$884$	33.9405	1.14154
$885$	−106.557	−3.58186
$886$	14.1536	0.475499
$887$	−3.91265	−0.131374	−0.0656869	−	0.997840i	$-0.520924\pi$
$887$	−3.91265	−0.131374	−0.0656869	+	0.997840i	$0.520924\pi$
$888$	−26.2513	−0.880935
$889$	25.5717	0.857648
$890$	−36.7341	−1.23133
$891$	31.8206	1.06603
$892$	−18.4166	−0.616634
$893$	14.8694	0.497584
$894$	47.2455	1.58013
$895$	−11.2976	−0.377639
$896$	4.99294	0.166803
$897$	−157.048	−5.24366
$898$	−8.15896	−0.272268
$899$	60.9629	2.03323
$900$	36.0914	1.20305
$901$	4.40376	0.146711
$902$	0.533742	0.0177717
$903$	−9.07665	−0.302052
$904$	6.00200	0.199624
$905$	−32.5877	−1.08325
$906$	52.2159	1.73476
$907$	−13.3890	−0.444575	−0.222288	−	0.974981i	$-0.571352\pi$
$907$	−13.3890	−0.444575	−0.222288	+	0.974981i	$0.571352\pi$
$908$	16.5122	0.547977
$909$	−29.4751	−0.977627
$910$	87.2607	2.89266
$911$	30.6241	1.01462	0.507311	−	0.861763i	$-0.330640\pi$
$911$	30.6241	1.01462	0.507311	+	0.861763i	$0.330640\pi$
$912$	−7.64966	−0.253306
$913$	2.69238	0.0891047
$914$	22.5384	0.745505
$915$	44.9920	1.48739
$916$	1.49450	0.0493798
$917$	83.3841	2.75359
$918$	100.670	3.32261
$919$	−31.1174	−1.02647	−0.513234	−	0.858249i	$-0.671553\pi$
$919$	−31.1174	−1.02647	−0.513234	+	0.858249i	$0.671553\pi$
$920$	−25.6020	−0.844073
$921$	−16.9933	−0.559948
$922$	6.70832	0.220927
$923$	16.7122	0.550088
$924$	16.6069	0.546328
$925$	−35.3292	−1.16162
$926$	0.00136530	4.48666e−5 0
$927$	21.9165	0.719832
$928$	−6.11844	−0.200848
$929$	30.9049	1.01396	0.506979	−	0.861958i	$-0.330762\pi$
$929$	30.9049	1.01396	0.506979	+	0.861958i	$0.330762\pi$
$930$	102.018	3.34530
$931$	41.2361	1.35146
$932$	20.4656	0.670373
$933$	−26.2903	−0.860705
$934$	−6.43527	−0.210569
$935$	18.4032	0.601850
$936$	−45.7752	−1.49621
$937$	49.7816	1.62629	0.813147	−	0.582059i	$-0.197753\pi$
$937$	49.7816	1.62629	0.813147	+	0.582059i	$0.197753\pi$
$938$	30.2378	0.987298
$939$	81.3568	2.65498
$940$	19.9022	0.649140
$941$	−33.7624	−1.10062	−0.550312	−	0.834959i	$-0.685491\pi$
$941$	−33.7624	−1.10062	−0.550312	+	0.834959i	$0.685491\pi$
$942$	−22.3179	−0.727156
$943$	−4.43901	−0.144554
$944$	10.4071	0.338721
$945$	258.822	8.41947
$946$	0.546558	0.0177701
$947$	−45.7239	−1.48583	−0.742914	−	0.669387i	$-0.766557\pi$
$947$	−45.7239	−1.48583	−0.742914	+	0.669387i	$0.766557\pi$
$948$	18.7850	0.610109
$949$	−60.6856	−1.96994
$950$	−10.2950	−0.334014
$951$	−31.6647	−1.02680
$952$	29.8492	0.967417
$953$	2.84913	0.0922923	0.0461462	−	0.998935i	$-0.485306\pi$
$953$	2.84913	0.0922923	0.0461462	+	0.998935i	$0.485306\pi$
$954$	−5.93930	−0.192292
$955$	−31.7060	−1.02598
$956$	27.1703	0.878749
$957$	−20.3504	−0.657836
$958$	−2.52588	−0.0816074
$959$	−0.282420	−0.00911982
$960$	−10.2389	−0.330458
$961$	68.2773	2.20249
$962$	44.8085	1.44468
$963$	88.2485	2.84377
$964$	9.24820	0.297865
$965$	−46.7393	−1.50459
$966$	−138.116	−4.44382
$967$	10.6760	0.343318	0.171659	−	0.985156i	$-0.445087\pi$
$967$	10.6760	0.343318	0.171659	+	0.985156i	$0.445087\pi$
$968$	−1.00000	−0.0321412
$969$	−45.7317	−1.46911
$970$	44.2355	1.42032
$971$	−47.3027	−1.51801	−0.759007	−	0.651082i	$-0.774315\pi$
$971$	−47.3027	−1.51801	−0.759007	+	0.651082i	$0.774315\pi$
$972$	−55.3198	−1.77438
$973$	64.8830	2.08005
$974$	7.56628	0.242439
$975$	−84.5264	−2.70701
$976$	−4.39424	−0.140656
$977$	−39.3377	−1.25852	−0.629262	−	0.777193i	$-0.716643\pi$
$977$	−39.3377	−1.25852	−0.629262	+	0.777193i	$0.716643\pi$
$978$	−5.12682	−0.163938
$979$	11.9330	0.381381
$980$	55.1934	1.76309
$981$	−20.6882	−0.660523
$982$	13.7731	0.439519
$983$	−54.3378	−1.73311	−0.866553	−	0.499084i	$-0.833670\pi$
$983$	−54.3378	−1.73311	−0.866553	+	0.499084i	$0.833670\pi$
$984$	−1.77527	−0.0565935
$985$	−3.07836	−0.0980846
$986$	−36.5777	−1.16487
$987$	107.368	3.41755
$988$	13.0573	0.415407
$989$	−4.54560	−0.144542
$990$	−24.8202	−0.788838
$991$	−29.8911	−0.949524	−0.474762	−	0.880114i	$-0.657466\pi$
$991$	−29.8911	−0.949524	−0.474762	+	0.880114i	$0.657466\pi$
$992$	−9.96380	−0.316351
$993$	18.6927	0.593195
$994$	14.6976	0.466179
$995$	−24.7404	−0.784323
$996$	−8.95507	−0.283752
$997$	37.4777	1.18693	0.593465	−	0.804860i	$-0.297759\pi$
$997$	37.4777	1.18693	0.593465	+	0.804860i	$0.297759\pi$
$998$	−20.5814	−0.651492
$999$	132.905	4.20494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.h.1.1	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.h.1.1	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.32608 q^{3} +1.00000 q^{4} +3.07836 q^{5} +3.32608 q^{6} -4.99294 q^{7} -1.00000 q^{8} +8.06282 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.32608 q^{3} +1.00000 q^{4} +3.07836 q^{5} +3.32608 q^{6} -4.99294 q^{7} -1.00000 q^{8} +8.06282 q^{9} -3.07836 q^{10} +1.00000 q^{11} -3.32608 q^{12} +5.67732 q^{13} +4.99294 q^{14} -10.2389 q^{15} +1.00000 q^{16} +5.97827 q^{17} -8.06282 q^{18} +2.29990 q^{19} +3.07836 q^{20} +16.6069 q^{21} -1.00000 q^{22} +8.31678 q^{23} +3.32608 q^{24} +4.47627 q^{25} -5.67732 q^{26} -16.8393 q^{27} -4.99294 q^{28} +6.11844 q^{29} +10.2389 q^{30} +9.96380 q^{31} -1.00000 q^{32} -3.32608 q^{33} -5.97827 q^{34} -15.3701 q^{35} +8.06282 q^{36} -7.89255 q^{37} -2.29990 q^{38} -18.8832 q^{39} -3.07836 q^{40} -0.533742 q^{41} -16.6069 q^{42} -0.546558 q^{43} +1.00000 q^{44} +24.8202 q^{45} -8.31678 q^{46} +6.46522 q^{47} -3.32608 q^{48} +17.9295 q^{49} -4.47627 q^{50} -19.8842 q^{51} +5.67732 q^{52} +0.736628 q^{53} +16.8393 q^{54} +3.07836 q^{55} +4.99294 q^{56} -7.64966 q^{57} -6.11844 q^{58} +10.4071 q^{59} -10.2389 q^{60} -4.39424 q^{61} -9.96380 q^{62} -40.2572 q^{63} +1.00000 q^{64} +17.4768 q^{65} +3.32608 q^{66} +6.05610 q^{67} +5.97827 q^{68} -27.6623 q^{69} +15.3701 q^{70} +2.94367 q^{71} -8.06282 q^{72} -10.6891 q^{73} +7.89255 q^{74} -14.8884 q^{75} +2.29990 q^{76} -4.99294 q^{77} +18.8832 q^{78} -5.64779 q^{79} +3.07836 q^{80} +31.8206 q^{81} +0.533742 q^{82} +2.69238 q^{83} +16.6069 q^{84} +18.4032 q^{85} +0.546558 q^{86} -20.3504 q^{87} -1.00000 q^{88} +11.9330 q^{89} -24.8202 q^{90} -28.3465 q^{91} +8.31678 q^{92} -33.1404 q^{93} -6.46522 q^{94} +7.07992 q^{95} +3.32608 q^{96} -14.3699 q^{97} -17.9295 q^{98} +8.06282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

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